﻿<p> </p>
<blockquote class="extDef">NOTE&nbsp; Definition according to ISO/CD 10303-42:1992<br>
A loop is a topological entity constructed from a single vertex, or by stringing together connected
(oriented) edges, or linear segments beginning and ending at the same vertex. It is typically used to bound a face lying on a surface. A loop has
dimensionality of 0 or 1. The domain of a 0-dimensional loop is a single point. The domain of a 1-dimensional loop is a connected, oriented curve, but need not
to be manifold. As the loop is a circle, the location of its beginning/ending point is arbitrary. The domain of the loop includes its bounds, an 0 &le; &Xi;
&lt; &infin;. 
A loop is represented by a single vertex, or by an ordered collection of oriented edges, or by an ordered collection of points. A loop is a graph, so
<em>M</em> and the graph genus <em>G<sup>l</sup></em> may be determined by the graph traversal algorithm. Since <em>M</em> = 1, the Euler equation (1) reduces
in this case to  
<blockquote><img src="../../../figures/ifcloop-math1.gif" height="31" width="180"></blockquote> 
where <em>V</em> and <em>E<sub>l</sub></em> are the number of unique vertices and oriented edges in the loop and <em>G<sup>l</sup></em> is the genus of the loop.
</blockquote> 

<blockquote class="note">NOTE&nbsp; Entity adapted from <strong>loop</strong> defined in ISO 10303-42.</blockquote>
<blockquote class="history">HISTORY&nbsp; New entity in IFC2x.</blockquote> 
<p class="spec-head">Informal Propositions:</p> 
<ol> 
 <li>A loop has a finite extent.</li> 
 <li>A loop describes a closed (topological) curve with coincident start and end vertices.</li> 
</ol>